BIMSA > Category and Topological Order Seminar Category and Topological Order Seminar Noninvertible surfaces, topological orders, and the 2-Deligne theorem
Noninvertible surfaces, topological orders, and the 2-Deligne theorem
Organizer
Hao Zheng
Speaker
Matthew Yu
Time
Tuesday, May 23, 2023 9:00 AM - 11:00 AM
Venue
Online
Abstract
Fusion higher categories have recently been of interest for their ability to describe the topological content of quantum field theories. I will focus on the notion of what is an anomaly for a noninvertible symmetry enacted by surface operators of a 2-category. I will then give examples of when we have reasonable control over these anomalies. In describing this I will introduce techniques that are also applicable for classifying 5d topological orders, and I will present the full classification. Finally I will present a result about fiber 2-functors which categorifies a theorem of Deligne's for symmetric 1-categories.
Speaker Intro
Matthew Yu is a postdoc at the mathematical institute at the University of Oxford. Before that, he earned his PhD at the University of Waterloo, while working at the Perimeter Institute for theoretical physics. He focuses on studying mathematical aspects of quantum field and string theory, bringing in ideas of homotopy theory and higher (fusion) categories.